Question

Income & Subtitution Effects, Deriving Market Demand

2. Suppose Josh's preference for pancakes and cereal are represented by U=XY. Initially he has I=20, the price of pancakes is $4/ each, and the price of cereal is $2/ bowl. His optimal consumption bundle initially is 5 cereal bowls and 2.5 pancakes. Suppose next that cereal is on sale this week, so its price drops to $1/bowl. Now Josh buys 6.7 cereals and 1.6 pancakes. His cereal consumption increased from 5 to 6.7 due to the price drop of cereal. Calculate the size of the substitution effect.. 3. Suppose the market for flying cars has only two customers. Bill's demand is given by Q=16-8P, Elon's demand is given by Q=15-5P, what's the market demand for flying cars?

Answer 1

Solution: (@) Gimn vaxy I=20 Pancarel Price = 84 each Cereal price = $2 / bowl. optimal consumption bundle is = 5 cereals 2.5pancakes If cereal is on sale this week, price drop = $11 bowl. Josh boys = 6.7 Cereals & 1.6 pancakes. Cercal Consumption increases = 5 to 6.7 Size of substitution effect is: - UzXY x = pancake MAS = moment I y a cereal. muy At optimality ya 200 = 2:5 and (x=5)

Utility = 5(2.5) =119.5] At new price a = 4 - Чу U = 19.5 = 4x2 x² = 3.125 :: X = 1.764-) Y = 4(1.7677) :: Y = 7.0710 point B is substitution effect Hence point A to